The crystal disappears from Bert's desk when he explains that it's quartz. His arms are below the desk so it could be in his hand however in the next shot his hands are still hidden but the crystal is back on the desk.
Since Leonard would have physical access to the WiFi router, he could simply reset it to default and change the password to what ever he wants.
In The Leftover Thermalization (2015), it was established that the cable bill was in Sheldon's name, not Leonard's. That being the case, it is likely that Sheldon moved the router to his and Amy's apartment when he moved across the hall.
In The Leftover Thermalization (2015), it was established that the cable bill was in Sheldon's name, not Leonard's. That being the case, it is likely that Sheldon moved the router to his and Amy's apartment when he moved across the hall.
Amy and Sheldon lock Penny and Leonard out of their WiFi but since they all have smartphones that means they all could still use the internet through their data plan with their respective cell phone carriers.